Eigenspaces
acs
Goal
from a selection of possible subset/chosen ESMs, come up with a metric for each of thoes subsets that says how good the subset is at representing the ‘truth’ that is the PCA of all of the CMIP6 data.
Then select the subset of ESMs with the smallest value for that metric and those are our ‘curated archive’ ESMs.
Work below covers 2 different metrics:
- The projection of all CMIP6 data into the first N eigenvectors from the PCA of all data vs projection of all CMIP6 data into the first N eigenvectors from the PCA of the subset data. Calculate NRMS between those two projections for each CMIP6 esmXscenario. Metric is the average value of all of those NRMS’s.
- saying for each subset of 5 ESMs, how similar is all CMIP6 data projected into that subset’s space vs projected into the ‘true’ space
- The coefficients of all CMIP6 data into the first N eigenvectors from the PCA of all data. For each of the OOS esmXscenarios, for each subset ESM, calculate the smallest L2 distance from the coefficients across the subset ESM’s scenarios= how close each subset ESM can get to every out of sample data point. Then take the minimum across subset ESMs = how close the selected subset can get to each OOS data point. The average of that distance from all OOS data points is then the metric for that subset.
- could weight by amount of variance explained by each dimension.
set up
And some package and labeling info
library(ggplot2)
library(dplyr)##
## Attaching package: 'dplyr'## The following objects are masked from 'package:stats':
##
## filter, lag## The following objects are masked from 'package:base':
##
## intersect, setdiff, setequal, unionlibrary(tidyr)
timeseries_dir <- 'extracted_timeseries/'
metrics_write_dir <- 'extracted_timeseries/extracted_metrics/'
# strawman subset of ESMs from our original 12, have all 4 experiments each
subset <- c('ACCESS-ESM1-5', 'CAMS-CSM1-0' , 'CMCC-CM2-SR5','GFDL-ESM4', 'MRI-ESM2-0')
subset2 <- c('ACCESS-CM2',
'ACCESS-ESM1-5',
'BCC-CSM2-MR',
'MIROC6', 'MRI-ESM2-0' )
# ESMS that dont have 4 experiments
non_candidate_esm <- c("CIESM",
"E3SM-1-1", "FIO-ESM-2-0", "GFDL-CM4", "IITM-ESM",
"IPSL-CM5A2-INCA", "KIOST-ESM", "NESM3", "NorESM2-LM")Load ESM data that’s been processed
region_summary_main <- read.csv(paste0(metrics_write_dir, 'IPCC_land_regions_metrics.csv'),
stringsAsFactors = FALSE)
region_summary_main %>%
filter(experiment != 'ssp119',
experiment != 'ssp434',
experiment != 'ssp460',
experiment != 'ssp534-over',
!(esm %in% non_candidate_esm)) %>% # remove from the full set of data
# that creates our 'true' CMIP6 PCA space
rename(region = acronym) ->
region_summary
print(head(region_summary))## esm experiment ensemble variable type name region
## 1 ACCESS-CM2 ssp126 r1i1p1f1 pr Land Arabian-Peninsula ARP
## 2 ACCESS-CM2 ssp126 r1i1p1f1 pr Land Central-Africa CAF
## 3 ACCESS-CM2 ssp126 r1i1p1f1 pr Land-Ocean Caribbean CAR
## 4 ACCESS-CM2 ssp126 r1i1p1f1 pr Land C.Australia CAU
## 5 ACCESS-CM2 ssp126 r1i1p1f1 pr Land C.North-America CNA
## 6 ACCESS-CM2 ssp126 r1i1p1f1 pr Land E.Asia EAS
## iasd end_val end_anomaly end_anomaly_pct mid_century_val
## 1 7.227917e-07 1.700625e-06 4.306991e-07 0.339153029 2.051770e-06
## 2 3.009324e-06 4.828026e-05 -4.965491e-08 -0.001027416 4.941042e-05
## 3 6.106140e-06 3.052769e-05 2.089845e-07 0.006892922 3.429079e-05
## 4 2.830779e-06 1.130480e-05 -1.269868e-06 -0.100986213 1.126320e-05
## 5 2.861294e-06 3.232150e-05 1.953880e-06 0.064340892 3.222543e-05
## 6 2.687448e-06 5.449186e-05 5.826705e-06 0.119730531 5.260652e-05
## mid_anomaly mid_anomaly_pct
## 1 7.818446e-07 0.61566180
## 2 1.080502e-06 0.02235680
## 3 3.972086e-06 0.13101110
## 4 -1.311461e-06 -0.10429388
## 5 1.857811e-06 0.06117738
## 6 3.941364e-06 0.08098944Prep data for PCA
# reshape:
grouped_data <- split(region_summary, list(region_summary$esm, region_summary$experiment))
grouped_data <- grouped_data[sapply(grouped_data, function(x) dim(x)[1]) > 0]
shaped_data <- lapply(grouped_data, function(group){
if (nrow(group) >0) {
group %>%
filter(variable == 'tas') %>%
select(esm, experiment, ensemble,type, region,
iasd, end_anomaly, mid_anomaly) %>%
rename(tas_iasd = iasd,
tas_end_anomaly = end_anomaly,
tas_mid_anomaly = mid_anomaly) %>%
left_join(group %>%
filter(variable == 'pr') %>%
select(esm, experiment, ensemble,type, region,
iasd, end_anomaly_pct, mid_anomaly_pct) %>%
rename(pr_iasd = iasd,
pr_end_anomaly_pct = end_anomaly_pct,
pr_mid_anomaly_pct = mid_anomaly_pct),
by = c('esm','experiment', 'ensemble', 'type', 'region')
) ->
reshaped
reshaped %>%
group_by(esm, experiment, type, region) %>%
summarize(tas_iasd=mean(tas_iasd),
tas_end_anomaly=mean(tas_end_anomaly, na.rm = T),
tas_mid_anomaly = mean(tas_mid_anomaly, na.rm = T),
pr_iasd = mean(pr_iasd, na.rm = T),
pr_end_anomaly_pct = mean(pr_end_anomaly_pct, na.rm = T),
pr_mid_anomaly_pct = mean(pr_mid_anomaly_pct, na.rm = T) ) %>%
ungroup() %>%
mutate(ensemble = 'ensemble_avg') -> #%>%
#bind_rows(reshaped) ->
reshaped2
#TODO need to change shaping if including ensemble members
reshaped2 %>%
select(-type) %>%
gather(metric, value, -esm, -experiment, -ensemble, -region) %>%
mutate(row_id = paste0(region, '~', metric),
col_id = paste0(esm, '~', experiment, '~', ensemble)) %>%
select(-esm, -experiment,-ensemble, -region, -metric) %>%
as.data.frame() ->
reshaped3
colnames(reshaped3) <- c(paste0(unique(reshaped3$col_id)), 'row_id', 'col_id')
rownames(reshaped3) <- paste0(reshaped3$row_id)
reshaped3 %>%
select(-col_id, -row_id) ->
out
return(out)
}
}
)
# combine columns but then transpose because prcomp wants rows to be observations
# and columns to be variables (but doing it the other way first is easier to code)
full_data <- t(do.call(cbind, shaped_data) )
# Drop anything with missing data
full_data1 <- na.omit(full_data)
print('removed rows due to missing data')## [1] "removed rows due to missing data"print(row.names(full_data)[c(which(!(row.names(full_data) %in% row.names(full_data1))))])## character(0)full_data <- as.data.frame(full_data1)
rm(full_data1)And the subsetted ESMs
as.data.frame(full_data) %>%
mutate(temp = row.names(.)) %>%
separate(temp, into=c('esm', 'trash'), sep = '~', extra='merge') %>%
filter(esm %in% subset) %>%
select(-esm, -trash) %>%
as.matrix(.) ->
subdataPCA
cmip6 ‘truth’
full_pca <- prcomp(full_data, center=TRUE, scale = TRUE)
# eigenspace from the PCA
full_eigenval <- data.frame(eigenvalues=(full_pca$sdev)^2)
full_eigenvec <- full_pca$rotation
# skree
var_explained_df <- data.frame(var_explained=(full_pca$sdev)^2/sum((full_pca$sdev)^2)) %>%
mutate(PC = as.integer(row.names(.)))
var_explained_df %>%
ggplot(aes(x=PC,y=var_explained, group=1))+
geom_point(size=4)+
geom_line()+
labs(title="Scree plot: PCA on scaled data - all ESMs")
pfull <- var_explained_df %>%
filter(PC <=15)%>%
ggplot(aes(x=PC,y=var_explained, group=1))+
geom_point(size=4)+
geom_line()+
labs(title="Scree plot: PCA on scaled data - all ESMs")
pfull 
subset
Functionalise from here, basically I think? :
sub_pca <- prcomp(subdata, center=TRUE, scale = TRUE)
# eigenspace from the PCA
sub_eigenval <- data.frame(eigenvalues=(sub_pca$sdev)^2)
sub_eigenvec <- sub_pca$rotation
# skree
var_explained_dfsub <- data.frame(var_explained=(sub_pca$sdev)^2/sum((sub_pca$sdev)^2)) %>%
mutate(PC = as.integer(row.names(.)))
var_explained_dfsub %>%
ggplot(aes(x=PC,y=var_explained, group=1))+
geom_point(size=4)+
geom_line()+
labs(title="Scree plot: PCA on scaled data - subset ESMs")
psub<- var_explained_dfsub %>%
filter(PC <=15)%>%
ggplot(aes(x=PC,y=var_explained, group=1))+
geom_point(size=4)+
geom_line()+
labs(title="Scree plot: PCA on scaled data - subset ESMs")
psub
side by side scree
pfull
psub
-> first five eigenvalues focus
Compare subset PCA space with full PCA space
differences in the projections of the same data
We’ve picked our subset of ESMs, so we project each available CMIP6 data row into:
- the first 5 eigenvectors of the full data
- the first 5 eigenvectors of the subset data
Then compare those projections.
then this will be repeated for every combination of 5 ESMs
Then pick the combo of 5 ESMs based on minimizing error for all observations.
Pro: don’t have to set a cutoff, can just select subset with smallest error
con: a lot of calculations
# project new data onto the PCA space
#TODO double check with fresher eyes
project_pca <- function(data, pca, n_eigenvalues=5){
# don't need this for full data on full pca, could just do pca$x[,1:n]
# but for full data on sub pca, do need this:
coeff <- scale(data, pca$center, pca$scale) %*% pca$rotation[,1:n_eigenvalues]
reconstructions <- sapply(1:nrow(data), function(rowindex){
reconstructed <- rowSums(sweep(pca$rotation[,1:n_eigenvalues],
MARGIN=2,
coeff[rowindex,],
`*`))
return(reconstructed)
})
colnames(reconstructions) <- rownames(data)
return(reconstructions)
}
# reconstruct the subdata in the space of first 5 eigenvectors of full data
recon_full <- project_pca(data = full_data, pca = full_pca, n_eigenvalues = 5)
# reconstruct the subdata in the space of first 5 eigenvectors of sub data
recon_sub <- project_pca(data = full_data, pca = sub_pca, n_eigenvalues = 5)
errs <- data.frame()
for (colindex in 1:ncol(recon_sub)){
sub <- recon_sub[, colindex]
full <- recon_full[,colindex]
bind_rows(data.frame(id = colnames(recon_sub)[colindex]) %>%
mutate(rms = sqrt(sum((sub - full)^2)) ,
nrms = rms /sqrt(sum((full)^2))) ,
errs) ->
errs
}
errs %>%
separate(id, into = c('esm', 'scenario', 'ensemble'), sep ='~') %>%
group_by(esm) %>%
summarize(avg_nrms_across_exps = mean(nrms)) %>%
ungroup ->
nrms
mean(nrms$avg_nrms_across_exps)## [1] 0.6572887compare coefficients in full PCA space
from the set of available coefficients in the full PCA space, select models whose coefficients span the space in the sense of:
every ESM is ‘close enough’ to one of the selected models in terms of L2 distance of coefficients
Pro: only need the full pca, not a pca of every candidate subset so fewer calculations
Con: have to decide on a cutoff
n_eigenvalues <- 5
coeff <- as.data.frame(full_pca$x[,1:n_eigenvalues])
# reshape so have info by ESM and experiment
coeff %>%
mutate(id = row.names(.)) %>%
separate(id, into = c('esm', 'scenario', 'ensemble'), sep ='~') %>%
gather(pc, value, -esm, -scenario, -ensemble) -> # %>%
# spread(scenario, value) ->
coeff_all_ESM
# pull off the subset coefficients into their own DF for comparison
coeff_all_ESM %>%
filter(esm %in% subset) %>%
spread(scenario, value) ->
coeff_sub_ESM
out <- data.frame()
for (esmname in unique(coeff_all_ESM$esm)){
if(!(esmname %in% subset)){
coeff_all_ESM %>%
filter(esm == esmname) ->
oos
# For each subset ESM, compare each oos scenario with all 4 scenarios
# and record the smallest. Then have a data frame with how close each
# subset ESM can get to each scenario of the oos ESM.
oos %>%
left_join(coeff_sub_ESM %>%
select(-ensemble) %>%
rename(subset_ESM = esm),
by = 'pc') %>%
group_by(esm, scenario, ensemble, subset_ESM) %>%
summarise(closest_L2 = min( sqrt(sum((value-ssp126)^2)),
sqrt(sum((value-ssp245)^2)),
sqrt(sum((value-ssp370)^2)),
sqrt(sum((value-ssp585)^2)))) %>%
ungroup %>%
# Then fillter to just the closest on each scenario
group_by(esm, scenario, ensemble) %>%
filter(closest_L2 == min(closest_L2)) %>%
ungroup %>%
bind_rows(out, .) ->
out
# If there is only one subset ESM that's closest for each scenario,
# obviously just pick that. But not sure where to go from there.
}
}
# take average L2 for all oos esms - that's the characteristic value for this
# particular subset. Then pick the subset that has smallest characteristic value.
mean(out$closest_L2)## [1] 7.035584may be the case that from a stitches perspective, we want to block compare ESM to ESM (so concatenate experiments into super vector of coeff) but how to handle ESMs that don’t have all the experiments for that comparison? if ACCESS is the oos ESM and didn’t do ssp245, we’d need to like find the ESM with the 3 most similar experiments, not necessarily just exclude 245 from the chosen
but also even oos ESM has all 4 experiments, why should we necessarily care about 245 being close to 245. Maybe 126 and 245 are close to 245 and that’s fine.
^ That’s what I’m doing but Can convince myself either way - one oos ESM-Exp combo being similar to one chosen ESM-Exp combo is enough for stitches to cover all behaviors; OR really need ESM to ESM comparison only
ESM selection
Then we would be brute force looping over eligible combinations of 5 ESMs (have all 4 scenarios, maybe some criteria on number ensemble members, and represent ECS distribution) and pick the one with either smallest vector differences = the axes are closest or the smallest projection differences.
Con of either method: not suitable for in-filling if decide to add an extra ESM but could probably be adapted? Like maybe we chose 5 so we want to see what the best ESM to add as 6 conditional on the 5 we already have would be? which may be different than the 6 best
30 ESMs in list total, 8 have a missing experiment
22 choose 5 = 26334 combinations (better than 30 choose 5, 142k)
we should aim to whittle down either on the front end by less than 22 - require some amount of ensemble members and/or represent ECS
functionalized
get_subset_data <- function(esmsubset, fulldata){
as.data.frame(fulldata) %>%
mutate(temp = row.names(.)) %>%
separate(temp, into=c('esm', 'trash'), sep = '~', extra='merge') %>%
filter(esm %in% esmsubset) %>%
select(-esm, -trash) %>%
as.matrix(.) ->
subdata
return(subdata)
}
project_pca <- function(data, pca, n_eigenvalues=5){
# don't need this for full data on full pca, could just do pca$x[,1:n]
# but for full data on sub pca, do need this:
coeff <- scale(data, pca$center, pca$scale) %*% pca$rotation[,1:n_eigenvalues]
reconstructions <- sapply(1:nrow(data), function(rowindex){
reconstructed <- rowSums(sweep(pca$rotation[,1:n_eigenvalues],
MARGIN=2,
coeff[rowindex,],
`*`))
return(reconstructed)
})
colnames(reconstructions) <- rownames(data)
return(reconstructions)
}
compare_projections <- function(fulldata, fullpca, subpca, n_eigenvalues = 5){
# reconstruct the subdata in the space of first 5 eigenvectors of full data
recon_full <- project_pca(data = fulldata,
pca = fullpca,
n_eigenvalues = n_eigenvalues)
# reconstruct the subdata in the space of first 5 eigenvectors of sub data
recon_sub <- project_pca(data = fulldata,
pca = subpca,
n_eigenvalues = n_eigenvalues)
# compare reconstructions
errs <- data.frame()
for (colindex in 1:ncol(recon_sub)){
sub <- recon_sub[, colindex]
full <- recon_full[,colindex]
bind_rows(data.frame(id = colnames(recon_sub)[colindex]) %>%
mutate(rms = sqrt(sum((sub - full)^2)) ,
nrms = rms /sqrt(sum((full)^2))) ,
errs) ->
errs
}
errs %>%
separate(id, into = c('esm', 'scenario', 'ensemble'), sep ='~') %>%
group_by(esm) %>%
summarize(avg_nrms_across_exps = mean(nrms)) %>%
ungroup ->
nrms
return(data.frame(avg_nrms_across_esms = mean(nrms$avg_nrms_across_exps)))
}
full_pca_distances <- function(subset_esms, fullpca, n_eigenvalues = 5){
coeff <- as.data.frame(fullpca$x[,1:n_eigenvalues])
# reshape so have info by ESM and experiment
coeff %>%
mutate(id = row.names(.)) %>%
separate(id, into = c('esm', 'scenario', 'ensemble'), sep ='~') %>%
gather(pc, value, -esm, -scenario, -ensemble) -> # %>%
# spread(scenario, value) ->
coeff_all_ESM
# pull off the subset coefficients into their own DF for comparison
coeff_all_ESM %>%
filter(esm %in% subset_esms) %>%
spread(scenario, value) ->
coeff_sub_ESM
out <- data.frame()
for (esmname in unique(coeff_all_ESM$esm)){
# only calculate for oos ESMs
if(!(esmname %in% subset_esms)){
coeff_all_ESM %>%
filter(esm == esmname) ->
oos
# For each subset ESM, compare each oos scenario with all 4 scenarios
# and record the smallest. Then have a data frame with how close each
# subset ESM can get to each scenario of the oos ESM.
oos %>%
left_join(coeff_sub_ESM %>%
select(-ensemble) %>%
rename(subset_ESM = esm),
by = 'pc') %>%
group_by(esm, scenario, ensemble, subset_ESM) %>%
summarise(closest_L2 = min( sqrt(sum((value-ssp126)^2)),
sqrt(sum((value-ssp245)^2)),
sqrt(sum((value-ssp370)^2)),
sqrt(sum((value-ssp585)^2)))) %>%
ungroup %>%
# Then filter to just the closest of any subset ESM
# on each oos scenario
group_by(esm, scenario, ensemble) %>%
filter(closest_L2 == min(closest_L2)) %>%
ungroup %>%
bind_rows(out, .) ->
out
# If there is only one subset ESM that's closest for each scenario,
# obviously just pick that. But not sure where to go from there.
} # end calculation for each subset esm
} # end loop over all ESMs
# take average L2 for all oos esms - that's the characteristic value for this
# particular subset. Then pick the subset that has smallest characteristic value.
return(data.frame(avg_closest_L2 = mean(out$closest_L2)))
}
########
# test functions
suppressMessages(compare_projections(fulldata = full_data,
fullpca = full_pca,
subpca = sub_pca,
n_eigenvalues = 5))## avg_nrms_across_esms
## 1 0.6572887suppressWarnings(suppressMessages(full_pca_distances(subset_esms = subset,
fullpca = full_pca,
n_eigenvalues = 5)))## avg_closest_L2
## 1 7.035584Test
Would load all the regional metric, reshape, do full PCA still.
Then suppose we have labeled subsets
table_of_subsets <- bind_rows(data.frame(subset_id = rep('subset1', 5),
subset = subset),
data.frame(subset_id = rep('subset2', 5),
subset = subset2))
knitr::kable(table_of_subsets)| subset_id | subset |
|---|---|
| subset1 | ACCESS-ESM1-5 |
| subset1 | CAMS-CSM1-0 |
| subset1 | CMCC-CM2-SR5 |
| subset1 | GFDL-ESM4 |
| subset1 | MRI-ESM2-0 |
| subset2 | ACCESS-CM2 |
| subset2 | ACCESS-ESM1-5 |
| subset2 | BCC-CSM2-MR |
| subset2 | MIROC6 |
| subset2 | MRI-ESM2-0 |
rm(subset)
rm(subset2)
rm(subdata)
rm(sub_pca)For each subset, calculate the two metrics.
metrics <- data.frame()
for (subsetid in unique(table_of_subsets$subset_id)){
subset <- table_of_subsets[table_of_subsets['subset_id']==subsetid,]$subset
get_subset_data(esmsubset = subset,
fulldata = full_data) ->
subdata
sub_pca <- prcomp(subdata, center=TRUE, scale = TRUE)
data.frame(subset_id = subsetid,
projection_metric = compare_projections(fulldata = full_data,
fullpca = full_pca,
subpca = sub_pca,
n_eigenvalues = 5),
coeff_metric = full_pca_distances(subset_esms = subset,
fullpca = full_pca,
n_eigenvalues = 5)) %>%
bind_rows(metrics, .)->
metrics
rm(subset)
rm(subdata)
rm(sub_pca)
}
write.csv(metrics, 'esm_subsets_metrics.csv', row.names = FALSE)all subsets
nESMs <- 5
region_summary %>%
select(esm) %>%
distinct %>%
filter(!(esm %in% non_candidate_esm)) ->
df
as.data.frame(t(apply(combn(nrow(df), nESMs),
2, function(i) df[i,])
)
) %>%
mutate(subset_id = paste0('subset', as.integer(row.names(.)))) %>%
gather(trash, subset, -subset_id) %>%
select(-trash) %>%
arrange(subset_id) ->
table_of_subsets
write.csv(table_of_subsets, 'subsets_22choose5.csv', row.names = FALSE)
# Table of all subsets with IDs
table_of_subsets <- read.csv('subsets_22choose5.csv')
table_of_subsets %>%
mutate(mod = as.integer(row.names(.)) %% 5,
esm=paste0('esm', mod)) %>%
select(-mod) %>%
spread(esm, subset) %>%
mutate(id = paste(esm1, esm2, esm3, esm4, esm0, sep='~')) ->
table_of_subsets2
# Table of ECS preserving subsets
ecs_subsets <- read.csv("five_sample_esm_climate_sensitivity.csv", stringsAsFactors = F)
ecs_subsets %>%
mutate(id = paste(esm1, esm2, esm3, esm4, esm5, sep='~')) %>%
gather(esm_id, esm, -cs1, -cs2, -cs3, -cs4, -cs5, -id ) %>%
gather(cs_id, cs, -esm_id, -esm, -id) %>%
mutate(esm_id2 = substr(esm_id, nchar(esm_id), nchar(esm_id)),
cs_id2 = substr(cs_id, nchar(cs_id), nchar(cs_id))) %>%
filter(esm_id2 == cs_id2) %>%
select(-esm_id, -cs_id, -esm_id2, -cs_id2) %>%
arrange(id) %>%
left_join(table_of_subsets2 %>% select(subset_id, id), by = 'id') %>%
select(subset_id, esm, cs) %>%
rename(subset=esm) %>%
na.omit()->
ecs_subsets_cleanmetrics <- data.frame()
for (subsetid in unique(ecs_subsets_clean$subset_id)){
subset <- ecs_subsets_clean[ecs_subsets_clean['subset_id']==subsetid,]$subset
get_subset_data(esmsubset = subset,
fulldata = full_data) ->
subdata
sub_pca <- prcomp(subdata, center=TRUE, scale = TRUE)
data.frame(subset_id = subsetid,
projection_metric = suppressMessages(compare_projections(fulldata = full_data,
fullpca = full_pca,
subpca = sub_pca,
n_eigenvalues = 5)),
coeff_metric = suppressWarnings(suppressMessages(full_pca_distances(subset_esms = subset,
fullpca = full_pca,
n_eigenvalues = 5)))) %>%
bind_rows(metrics, .)->
metrics
rm(subset)
rm(subdata)
rm(sub_pca)
}
write.csv(metrics, 'esm_subsets_metrics_22choose5_ECS.csv', row.names = FALSE)Take a look at minimizing sets of ESMs
# Metrics for every subset with IDs
metrics <- read.csv('esm_subsets_metrics_22choose5.csv') %>%
rename(projection_metric = avg_nrms_across_esms,
coefficient_metric = avg_closest_L2)
# Table of all subsets with IDs
table_of_subsets <- read.csv('subsets_22choose5.csv')
table_of_subsets %>%
mutate(mod = as.integer(row.names(.)) %% 5,
esm=paste0('esm', mod)) %>%
select(-mod) %>%
spread(esm, subset) %>%
mutate(id = paste(esm1, esm2, esm3, esm4, esm0, sep='~')) ->
table_of_subsets2
# Table of ECS preserving subsets
ecs_subsets <- read.csv("five_sample_esm_climate_sensitivity.csv", stringsAsFactors = F)
ecs_subsets %>%
mutate(id = paste(esm1, esm2, esm3, esm4, esm5, sep='~')) %>%
gather(esm_id, esm, -cs1, -cs2, -cs3, -cs4, -cs5, -id ) %>%
gather(cs_id, cs, -esm_id, -esm, -id) %>%
mutate(esm_id2 = substr(esm_id, nchar(esm_id), nchar(esm_id)),
cs_id2 = substr(cs_id, nchar(cs_id), nchar(cs_id))) %>%
filter(esm_id2 == cs_id2) %>%
select(-esm_id, -cs_id, -esm_id2, -cs_id2) %>%
arrange(id) %>%
left_join(table_of_subsets2 %>% select(subset_id, id), by = 'id') %>%
select(subset_id, esm, cs) %>%
rename(subset=esm) %>%
na.omit() ->
ecs_subsets_cleanminimize across all possible combinations
# Subset that is minimum in the projection metric across all possible subsets
metrics %>%
filter(projection_metric == min(projection_metric)) %>%
left_join(table_of_subsets, by = c('subset_id')) ->
projection_min
metrics %>%
filter(coefficient_metric == min(coefficient_metric)) %>%
left_join(table_of_subsets, by = c('subset_id')) ->
coefficient_min
knitr::kable(projection_min)
knitr::kable(coefficient_min)minimize across ECS-distribution
# Subset that is minimum in the projection metric across all possible subsets
metrics %>%
left_join(ecs_subsets_clean, by = c('subset_id')) %>%
na.omit %>%
filter(projection_metric == min(projection_metric)) ->
projection_min
metrics %>%
left_join(ecs_subsets_clean, by = c('subset_id')) %>%
na.omit %>%
filter(coefficient_metric == min(coefficient_metric)) ->
coefficient_min
knitr::kable(projection_min)| subset_id | projection_metric | coefficient_metric | subset | cs |
|---|---|---|---|---|
| subset7277 | 0.6439649 | 7.227339 | ACCESS-ESM1-5 | 3.90 |
| subset7277 | 0.6439649 | 7.227339 | CAMS-CSM1-0 | 2.30 |
| subset7277 | 0.6439649 | 7.227339 | CMCC-CM2-SR5 | 3.52 |
| subset7277 | 0.6439649 | 7.227339 | GFDL-ESM4 | 2.60 |
| subset7277 | 0.6439649 | 7.227339 | MRI-ESM2-0 | 3.20 |
knitr::kable(coefficient_min)| subset_id | projection_metric | coefficient_metric | subset | cs |
|---|---|---|---|---|
| subset159 | 0.791654 | 6.396746 | ACCESS-CM2 | 4.7 |
| subset159 | 0.791654 | 6.396746 | ACCESS-ESM1-5 | 3.9 |
| subset159 | 0.791654 | 6.396746 | BCC-CSM2-MR | 3.0 |
| subset159 | 0.791654 | 6.396746 | MIROC6 | 2.6 |
| subset159 | 0.791654 | 6.396746 | MRI-ESM2-0 | 3.2 |
plotting in full PCA space
full_pca$x %>%
as.data.frame() %>%
mutate(id = row.names(.)) %>%
separate(id, into=c('model', 'scenario', 'ensemble'), sep = '~') %>%
select(model, scenario, PC1, PC2, PC3, PC4, PC5, PC6)->
coordinatesall PCs
coordinates %>%
gather(pc_x, pc_x_val, -model, -scenario) %>%
left_join(coordinates %>%
gather(pc_y, pc_y_val, -model, -scenario),
by = c('model', 'scenario')) %>%
mutate(x_id = as.integer(substr(pc_x, nchar(pc_x), nchar(pc_x))),
y_id = as.integer(substr(pc_y, nchar(pc_y), nchar(pc_y)))) %>%
filter(y_id > x_id) ->
grid_plot## Warning in left_join(., coordinates %>% gather(pc_y, pc_y_val, -model, -scenario), : Detected an unexpected many-to-many relationship between `x` and `y`.
## ℹ Row 1 of `x` matches multiple rows in `y`.
## ℹ Row 1 of `y` matches multiple rows in `x`.
## ℹ If a many-to-many relationship is expected, set `relationship =
## "many-to-many"` to silence this warning.ggplot(data = grid_plot) +
geom_point(mapping = aes(x = pc_x_val, y = pc_y_val,
color = model, shape = scenario), size = 0.5) +
geom_point(data = grid_plot %>% filter(model %in% projection_min$subset),
mapping = aes(x = pc_x_val, y = pc_y_val, color = model, shape = scenario),
size = 2) +
ggtitle('PCA of full data, projection metric minimizers') +
facet_grid(pc_y ~ pc_x)
ggplot(data = grid_plot) +
geom_point(mapping = aes(x = pc_x_val, y = pc_y_val,
color = model, shape = scenario), size = 0.5) +
geom_point(data = grid_plot %>% filter(model %in% coefficient_min$subset),
mapping = aes(x = pc_x_val, y = pc_y_val, color = model, shape = scenario),
size = 2) +
ggtitle('PCA of full data, coefficient metric minimizers') +
facet_grid(pc_y ~ pc_x)
PC1 vs PC2
ggplot(coordinates) +
geom_point(mapping = aes(x = PC1, y = PC2, color = model, shape = scenario))+
ggtitle('PCA of full data')
p1 <- ggplot(coordinates) +
geom_point(mapping = aes(x = PC1, y = PC2, color = model, shape = scenario)) +
geom_point(data = coordinates %>% filter(model %in% projection_min$subset),
mapping = aes(x = PC1, y = PC2, color = model, shape = scenario),
size = 4) +
ggtitle('PCA of full data, projection metric minimizers')
p2 <- ggplot(coordinates) +
geom_point(mapping = aes(x = PC1, y = PC2, color = model, shape = scenario)) +
geom_point(data = coordinates %>% filter(model %in% coefficient_min$subset),
mapping = aes(x = PC1, y = PC2, color = model, shape = scenario),
size = 4) +
ggtitle('PCA of full data, coefficient metric minimizers')
gridExtra::grid.arrange(p1, p2)
PC1 vs PC3
p3 <- ggplot(coordinates) +
geom_point(mapping = aes(x = PC1, y = PC3, color = model, shape = scenario)) +
geom_point(data = coordinates %>% filter(model %in% projection_min$subset),
mapping = aes(x = PC1, y = PC3, color = model, shape = scenario),
size = 4) +
ggtitle('PCA of full data, projection metric minimizers')
p4 <- ggplot(coordinates) +
geom_point(mapping = aes(x = PC1, y = PC3, color = model, shape = scenario)) +
geom_point(data = coordinates %>% filter(model %in% coefficient_min$subset),
mapping = aes(x = PC1, y = PC3, color = model, shape = scenario),
size = 4) +
ggtitle('PCA of full data, coefficient metric minimizers')
gridExtra::grid.arrange(p3, p4)
PC3 vs PC4
gridExtra::grid.arrange(ggplot(coordinates) +
geom_point(mapping = aes(x = PC3, y = PC4, color = model, shape = scenario)) +
geom_point(data = coordinates %>% filter(model %in% projection_min$subset),
mapping = aes(x = PC3, y = PC4, color = model, shape = scenario),
size = 4) +
ggtitle('PCA of full data, projection metric minimizers, exclude MRI'),
ggplot(coordinates) +
geom_point(mapping = aes(x = PC3, y = PC4, color = model, shape = scenario)) +
geom_point(data = coordinates %>% filter(model %in% coefficient_min$subset),
mapping = aes(x = PC3, y = PC4, color = model, shape = scenario),
size = 4) +
ggtitle('PCA of full data, coefficient metric minimizers, exclude MRI'))
Validation
basic summary values
as.data.frame(full_data) %>%
mutate(id = row.names(.)) %>%
separate(id, into = c('esm', 'scenario', 'ensemble') , sep = '~') %>%
gather(metric, value, -esm, -scenario, -ensemble) %>%
separate(metric, into = c('region', 'metric'), sep = '~') %>%
spread(metric, value)->
full_df
full_df %>%
filter(esm %in% coefficient_min$subset) ->
sub_df
full_df %>%
group_by(region) %>%
summarize(cmip_pr_end_anomaly_pct = mean(pr_end_anomaly_pct),
cmip_pr_iasd = mean(pr_iasd),
cmip_pr_mid_anomaly_pct = mean(pr_mid_anomaly_pct),
cmip_tas_end_anomaly = mean(tas_end_anomaly),
cmip_tas_iasd = mean(tas_iasd),
cmip_tas_mid_anomaly = mean(tas_mid_anomaly)) %>%
ungroup ->
full_summary
sub_df %>%
group_by(region) %>%
summarize(sub_pr_end_anomaly_pct = mean(pr_end_anomaly_pct),
sub_pr_iasd = mean(pr_iasd),
sub_pr_mid_anomaly_pct = mean(pr_mid_anomaly_pct),
sub_tas_end_anomaly = mean(tas_end_anomaly),
sub_tas_iasd = mean(tas_iasd),
sub_tas_mid_anomaly = mean(tas_mid_anomaly)) %>%
ungroup ->
sub_summary
full_summary %>%
left_join(sub_summary, by = 'region') %>%
mutate(diff_pr_end_anomaly_pct = cmip_pr_end_anomaly_pct-sub_pr_end_anomaly_pct,
diff_pr_iasd = cmip_pr_iasd-sub_pr_iasd,
diff_pr_mid_anomaly_pct = cmip_pr_mid_anomaly_pct-sub_pr_mid_anomaly_pct,
diff_tas_end_anomaly = cmip_tas_end_anomaly-sub_tas_end_anomaly,
diff_tas_iasd = cmip_tas_iasd-sub_tas_iasd,
diff_tas_mid_anomaly = cmip_tas_mid_anomaly-sub_tas_mid_anomaly) ->
compare
max(abs(compare$diff_pr_end_anomaly_pct))## [1] 0.1025214max(abs(compare$diff_pr_iasd))## [1] 1.131961e-06max(abs(compare$diff_pr_mid_anomaly_pct))## [1] 0.04349838max(abs(compare$diff_tas_end_anomaly))## [1] 0.2323388max(abs(compare$diff_tas_iasd))## [1] 0.1125657max(abs(compare$diff_tas_mid_anomaly))## [1] 0.3092634HS notes
- Hawkins and Sutton 09/Lehner2020: do for full data, do for final subset of ESMs and compare?
From Lehner https://esd.copernicus.org/articles/11/491/2020/esd-11-491-2020.pdf
- T and P globally and regionally over time; and gridded for time slices
the model uncertainty M is calculated as the variance across the ensemble means of the seven SMILEs (i.e., across the forced responses of the SMILEs).
internal variability uncertainty I is calculated as the variance across ensemble members of a given SMILE, yielding one estimate of I per model. Prior to this calculation, time series are smoothed with the running mean corresponding to the target metric (here mostly decadal means). Averaging across the seven I values yields the multimodel mean internal variability uncertainty Imean. Alternatively, to explore the assumption that Imean does not change over time, we use the 1950–2014 average value of Imean throughout the calculation (i.e., Ifixed). We also use the model with the largest and smallest I , i.e., Imax and Imin, to quantify the e influence of model uncertainty in the estimate of I.
Following HS09, we calculate S as the variance across the multimodel means calculated for the different emissions scenarios, using a consistent set of available models.
Then how do I want to apply that to our IPCC regional metrics (ideally) or the full time series